Rooting a device is a method to gain full access to the operating system. With root you can do all the administrative stuff, write to locations normally restricted to the system and customize your device deeper.
Root enhances your privileges and you are able to change almost anything inside of your rom.
The rooting, however, affects ONLY your operating system (Android)
In most devices, the Bootloader is the instance that calls the operating system (Android) and manages direct access to the device's partitions. Having an unlocked bootloader enables you to flash custom roms, custom kernels, recoveries and so on.
Bootloader and Rooting Teamplay
Often it is the case, and so, too in our devices, that a locked bootloader also locks write access to several partitions like the system partition. This is the reason why rooting is not able without unlocked bootloader. Rooting needs write access to the system partition (for storing the superuser binary and the superuser app)
Without unlocked bootloader, only a temporary half-root can be achieved.
Please Search the forums
and ask your questions there. I'm no personal supporter.
HTC One (m7_ul)